Optimal solutions of a non-linear minimum fuel problem and minimum time orbital transfer problem, computed without prior knowledge of singular arcs' existence

Abstract

Abstract The General Search Algorithm (GSA) previously presented by Katz (1974) has been extended to cover fixed time minimum effort problems and minimum time problems, having possible singular arcs, in problems where there is no a priori knowledge of the singular arcs. The conditions on the control set, the differential equations of state, and the state and control constraints are similar to those in the previous work, as is the dependence of the local-minimum convergence proof upon assumed convergence of a substep algorithm (Katz 1974) for non-linear optimal regulator problems GSA is applied to two example problems, both having singular arcs. In the first of these (a fixed time minimum fuel problem having known reachable sot and optimal solution) the conditions of the convergence proof were satisfied throughout and GSA converged to the resulting approximation of an optimal solution, in repeated trials. The second example (a minimum time Saturn vehicle orbital injection problem) suffered from non-satisfa...